Question

plzz help me to find the domain and range of f(x) =-sqrt(-5-6x-x^2)

Answer 1

Well, start with -5-6x-x^2 >= 0 or 5 + 6x + x^2 <= 0

Answer 2

I got the domain D = [-5,-1] , not getting the range
got y^2=4 so it should be -2<=y<=2
but answer for range is [-2,0]

Answer 3

y is always negative, so it should be from [-2,0]

Answer 4

The Domain is Negative Only. You cannot get a positive number out of that.

Excellent job ont he Domain.

Answer 5

how do i write it ?
what should be my statements after y^2=4 or -2<=y<=2

Answer 6

well, there is a negative sign infront , so that makes the range always negative

Answer 7

No, that still have y > 0. Eliminate that part.

Answer 8

I want to frame the answer with right wordings
could you tell me what to write to arrive at Range [-2,0]

Answer 9

of course, i didn't get [-2,0] right off the bat.

Notice that
-sqrt(-5-6x-x^2 = -sqrt[4 - (x+3)^2)]

This is just a lower semi-circle whose center is at (-3,0) and with radius = 2.
That is how I got [-2,0]. I just assumed you knew this

Answer 10

the lower part :DD

Answer 11

We have a lovely parabola, y = -5-6x-x^2 = -(x+3)^2 + 4

Notice, with the vertex at (-3,4), we have the range \([-\infty,4)\).

Now, we're going to need to find the square root of that, so we discard any negative portion. Thus, the range is now \([0,4]\)

Once we find the square root (positive, unless otherwise stated), we find that the Range is now \([0,2]\)

Finally, some sadistic textbook author put a negative sign in front of this one, so we're stuck with a Range of \([-2,0]\)

You just have to walk through it.

Answer 12

Whoops, that first one should have been \((-\infty,4]\).